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Syllabus of Math 612, Section 600

Partial Differential Equations

Spring 2012

Instructor Peter Kuchment

Office Rm. Blocker 614A, Telephone (979)862-3257

E-mail:, Home Page: /~kuchment

Section: 600, Time: TR 9:35 am - 10:50 am, Room: ZACH 119D
Textbook: L. C. Evans, Partial Differential Equations: 2nd edition , American Math. Society, 2010.
Office hours: TR 11:00-noon, Blocker 614A
Additional office hours can be arranged by appointment.


This class is devoted to the theory of linear partial differential equations. Assuming some initial familiarity of students with PDEs, the following main topics will be addressed:

  1. Classification of equations of 2nd order

  2. Sobolev spaces

  3. Second order elliptic equations (including boundary value problems theory and spectral theory)

  4. Linear evolution equations (including parabolic and hyperbolic problems)

Besides numerous applications inside mathematics, the PDEs form the core part of our scientific understanding of the physical world: from physics to chemistry, to biology, to meteorology, you name it.

The class will be based on the second part "Theory for linear partial differential equations" of the well respected recent textbook by L. Evans.


MATH 611, its equivalent, or instructor's consent (if unsure, please contact the instructor).


Grading will be based on home assignments and a take-home final exam.

Tentative schedule of the course
(watch for updates)


Topics and sections

Home assignments


01/17 - 01/21

Classification of 2nd order PDEs.




Chapter 5: Sobolev spaces




Chapter 6: Elliptic problems



03/11- 03/17

Spring break

Have some rest :-)



Chapter 7: Evolution equations


Take home final


Percentage of points


90% and higher


80% and higher


70% and higher


60% and higher


Less than 60%


Recommended additional reading

Make-up policy:

Make-ups for missed quizzes, home assignments and exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistent with University Student Rules , students are required to notify an instructor by the end of the next working day after missing an exam or quiz. Otherwise, they forfeit their rights to a make-up.

Grade complaints:

Sometimes the instructor might make a mistake grading your work. If you feel that this has happened, you have one week since the graded work was handed back to you to talk to the instructor. If a mistake is confirmed, the grade will be changed. No complaints after that deadline will be considered.

Scholastic dishonesty:

Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. Collaboration on assignments, either in-class or out-of-class, is forbidden unless permission to do so is granted by your instructor. For more information on university policies regarding scholastic dishonesty, see University Student Rules .

Students with Disabilities:

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Services for Students with Disabilities, Koldus 126, 845-1637.

Copyright policy:

All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.


This syllabus is subject to change at the instructors' discretion

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Last revised January 11th, 2012